Question

Write an expression for the product (See picture) without a perfect square factor in the radicand.

Answer 1

Answer: 3x^2√10

Step-by-step explanation:

√6x * √15x^3

The product of roots with the same index is equal to the root, so

√6x * 15x^3

Calculate the sum inside the radical

√90x^4

Then, you can simplify the radical expression and move the variable+exponent

3x^2√10

Answer 2

The expression after product is $x^{2} \sqrt{90}$.

Option A is correct.

Radical expression:

The given expression is,

                           $\sqrt{6x} \cdot\sqrt{15x^{3} }$

We have to simplify above expression.

               $\sqrt{6x} \cdot\sqrt{15x^{3} }=\sqrt{15*6*x^{4} } \\\\\sqrt{6x} \cdot\sqrt{15x^{3} }=\sqrt{90*x^{4} } \\\\\sqrt{6x} \cdot\sqrt{15x^{3} }=x^{2} \sqrt{90}$

Hence. the expression after product is $x^{2} \sqrt{90}$.

Learn more about the radical expression here:

https://brainly.com/question/8952483